# Rational Equations Using Proportions

Rational equations using proportions form a fundamental aspect of algebra, providing a systematic approach to solving equations containing fractions. In these mathematical expressions, variables are embedded within ratios, and solving for unknowns involves cross-multiplication and simplification. This method is particularly useful in various real-world applications, such as solving problems related to rates, proportions, and scaling. Understanding how to manipulate rational equations using proportions not only enhances problem-solving skills but also lays a solid foundation for more advanced algebraic concepts.

Questions

- How do you solve #(y^2+5y-6)/(y^3-2y^2)=5/y-6/(y^3-2y^2)#?
- What is the solution set for #(x-2)/(x+4)=2-(4/x)#?
- How do you solve the proportion #8/m=32/52#?
- It takes Noah 3 hours to paint one side of a fence. It takes Gilberto 5 hours. How long would it take them if they worked together?
- What is the total cost of 0.5 pound of peaches selling for $0.80 per pound and 0.7 pound of oranges selling for $0.90 per pound?
- How do you solve #12/7=36/m#?
- How do you cross multiply #\frac{4x}{x+2}=\frac{5}{9}#?
- How do you solve #1.5:3 = x:12#?
- How do you solve #2/y=10/60#?
- How do you simplify #x/2 = 4/7#?
- How do you solve #(x/3) = (12/(x-5))#?
- How do you solve #4/(x-3)=4#?
- How do you solve the proportion #48/24=k/13#?
- How do you combine #1/2+2/(x+2)#?
- How do you solve #5/b=3/9#?
- Five friends order sandwiches at a restaurant. Each person orders either a turkey or a ham sandwich. The turkey costs $2.50 and the ham costs $3.00. If the bill is $14.00 without tax or tip, how many sandwiches of each type did the group purchase?
- How do you solve the proportion #(x-1)/4 = 5/(x+7)#?
- How do you solve #(x +2) / 3 = 6/ (x-1)#?
- How do you solve #9/g=15/10#?
- I need to find the amount of money the fourth teacher pay. See picture! Thanks?!